Controlled Markov Processes and Viscosity SolutionsThis book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. |
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Results 1-3 of 90
Page 35
... constant , ( s ) = constant , which is in accord with what was just shown about minimizing extremals x * ( · ) . Control until exit from Q. As in Section 3 , class B , let us now consider the calculus of variations problem of minimizing ...
... constant , ( s ) = constant , which is in accord with what was just shown about minimizing extremals x * ( · ) . Control until exit from Q. As in Section 3 , class B , let us now consider the calculus of variations problem of minimizing ...
Page 118
... constant K3 such that ( 16.11 ) 0 ≤ V ( t , x ) ≤ K3 distance ( x , 0 ) , ( t , x ) € Q . Indeed fix ( t , x ) Є Q and choose z Є 00 satisfying | x - z = distance ( x , 80 ) . Let 8 > 0 be as in ( 10.6 ) . Set u = 8 ( x − x ) / | z ...
... constant K3 such that ( 16.11 ) 0 ≤ V ( t , x ) ≤ K3 distance ( x , 0 ) , ( t , x ) € Q . Indeed fix ( t , x ) Є Q and choose z Є 00 satisfying | x - z = distance ( x , 80 ) . Let 8 > 0 be as in ( 10.6 ) . Set u = 8 ( x − x ) / | z ...
Page 155
... constant con- trols . If t1t Mh , M = 1 , 2 , ... , let = Vh ( t , x ) = Th_t ( x ) . - Then Vh ( t , x ) turns out to be the value function obtained by requiring that u ( s ) is constant on each interval ( t + mh , t + ( m + 1 ) h ] ...
... constant con- trols . If t1t Mh , M = 1 , 2 , ... , let = Vh ( t , x ) = Th_t ( x ) . - Then Vh ( t , x ) turns out to be the value function obtained by requiring that u ( s ) is constant on each interval ( t + mh , t + ( m + 1 ) h ] ...
Other editions - View all
Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner Limited preview - 2006 |
Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner No preview available - 2006 |
Common terms and phrases
admissible control assume assumptions boundary condition boundary data bounded brownian motion C₁ Cą(Q calculus of variations Chapter classical solution consider continuous on Q controlled Markov diffusion convergence convex Corollary D₂V defined definition denote deterministic dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite formula Hence HJB equation holds implies inequality initial data lateral boundary Lebesgue Lemma lim sup linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal Markov control partial derivatives partial differential equation proof of Theorem prove reference probability system Remark result satisfies second-order Section semiconvex stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields